# Bowtie-free graphs and generic automorphisms

## TL;DR

This paper proves that the countable universal omega-categorical bowtie-free graph has generic automorphisms and is not finitely homogenisable, contributing to the understanding of automorphism groups in specific graph classes.

## Contribution

It establishes the existence of generic automorphisms in the bowtie-free graph and demonstrates that it is not finitely homogenisable, advancing knowledge in model theory and graph automorphisms.

## Key findings

- The countable universal omega-categorical bowtie-free graph admits generic automorphisms.
- This graph is not finitely homogenisable.
- The results deepen understanding of automorphism groups in specific graph classes.

## Abstract

We show that the countable universal omega-categorical bowtie-free graph admits generic automorphisms. Moreover, we show that this graph is not finitely homogenisable.